Learning Continuous Normalizing Flows For Faster Convergence To Target Distribution via Ascent Regularizations

Normalizing flows (NFs) have been shown to be advantageous in modeling complex distributions and improving sampling efficiency for unbiased sampling. In this work, we propose a new class of continuous NFs, ascent continuous normalizing flows (ACNFs), that makes a base distribution converge faster to a target distribution. Although solving such a flow is non-trivial and barely possible, we propose a practical implementation to learn flexibly parametric ACNFs via ascent regularization and apply in two learning cases: maximum likelihood learning for density estimation and minimizing reverse KL divergence for unbiased sampling and variational inference. The learned ACNFs demonstrate faster convergence towards the target distributions, therefore, achieving better density estimations, unbiased sampling and variational approximation at lower computational cost. Furthermore, the flows show to stabilize themselves to mitigate performance deterioration and are less sensitive to the choice of training flow length $T$ .